There can be coexisting slow and fast degrees of freedom
in a single quantum system.
In the Born-Oppenheimer approximation (BOA for short),
the slow degrees of freedom are regarded as frozen,
i.e. their kinetic energy is dropped,
when the Schrödinger equation of the fast degrees of freedom
is solved [1]}. The energy eigenvalues and eigenfunctions of the fast degrees of freedom are functions of the slow coordinates and
the energy eigenvalue acts as a potential energy for the
slow degrees of freedom.
